Exit asymptotics for small diffusion about an unstable equilibrium

Adsorption relaxation for nonionic surfactants under mixed barrier-diffusion and micellization-diffusion control.

Relaxation processes of surfactant adsorption and surface tension, which are characterized by two specific relaxation times, are theoretically investigated. We are dealing with fluid interfaces and small initial deviations from equilibrium. For surfactant concentrations below the critical micellization concentration (CMC), we consider adsorption under mixed barrier-diffusion control. General an...

Exit Time and Invariant Measure Asymptotics for Small Noise Constrained Diffusions

Constrained diffusions, with diffusion matrix scaled by small > 0, in a convex polyhedral cone G ⊂ R, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B ⊂ G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as → 0, the moments of functionals of exit lo...

Metastability in Reversible Diffusion Processes I. Sharp Asymptotics for Capacities and Exit Times

Numerical Schemes for Kinetic Equations in the Anomalous Diffusion Limit. Part I: The Case of Heavy-Tailed Equilibrium

Abstract. In this work, we propose some numerical schemes for linear kinetic equations in the anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion type equation. However, when a heavy-tailed distribution is considered, another time scale is...

Scaling Limits for Conditional Diffusion Exit Problems and Asymptotics for Nonlinear Elliptic Equations

The goal of this paper is to supplement the large deviation principle of the Freidlin–Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind. Namely, we describe a class of situations where conditioning on exit through unlikely locations leads to a Gaussian scaling limit for the exit distribution. Our results are based on Doob’s h-transform...